Using Region-X assigned IP space in Region-Y?

[mark at bernoullinetworks.com (Mark Leonard)]

Hello NANOG'ers,

This is a question that popped into my mind recently.  So far my google-fu
has not turned up anything of use.

Imagine a company that has an RIR-assigned IPv4/23, and has it subnetted
into a pair of /24's so that they can have replicated datacenters in two
different geographical locations each running its own BGP infrastructure
(using the same ASN).

As far as I can see, this is all fine and good assuming that these two
sites are in the same RIR's domain.

Is it possible/allowable to move one of these datacenters to a different
geographical region with a different RIR and keep using the same two
subnets, or will a new /24 need to be requested from the new RIR?

If there's a book or reference that answers this question, please let me
know - I'm willing to do as much research on my own as I can.

Thanks!